You couldn't imagine innocent people changing their stories - but it happens. So what does that say about the validity of your inference from your own imagination to the expected behaviour of other people?

I didn't see the above when I first read your comment; maybe I was busy forming, mentally, my reply, below, to the rest of what you said. I direct you to the comment I just posted, at 02 February 2014 11:49:15PM, in response to Wes_W.

I also doubt that criminalisation would change much.

It wouldn't hurt.

I'm also not sure what's supposed to be so extremely antisocial about it. It's not like the police will surely catch the responsible party if only you don't make that false confession to get a more lenient sentence.

Presumably, a false confession increases the likelihood that a case will be erroneously closed. That, in my estimation, makes it extremely antisocial, not least because it increases the likelihood that a criminal is not only at large but is unrecognized as such. Every person is obliged to avoid giving his or her fellow human beings false information about crime.